At the Party:

• There were 9 men and children.
• There were 2 more women than children
• The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.

Also, of the three groups - men, women and children - at the party:

• There were 4 of one group.
• There were 6 of one group.
• There were 8 of one group.

Exactly one of the above 6 statements is false.

Which one of the above statements is false? Also, how many men, women and children are there at the party?